3
\includegraphics[max width=\textwidth, alt={}, center]{9f17f7b8-b54d-467d-be26-21c599ce6ca2-2_515_750_669_699} In the diagram \(O C A\) and \(O D B\) are radii of a circle with centre \(O\) and radius \(2 r \mathrm {~cm}\). Angle \(A O B = \alpha\) radians. \(C D\) and \(A B\) are arcs of circles with centre \(O\) and radii \(r \mathrm {~cm}\) and \(2 r \mathrm {~cm}\) respectively. The perimeter of the shaded region \(A B D C\) is \(4.4 r \mathrm {~cm}\).

1. Find the value of \(\alpha\).
2. It is given that the area of the shaded region is \(30 \mathrm {~cm} ^ { 2 }\). Find the value of \(r\).
   \(4 C\) is the mid-point of the line joining \(A ( 14 , - 7 )\) to \(B ( - 6,3 )\). The line through \(C\) perpendicular to \(A B\) crosses the \(y\)-axis at \(D\).